In tests I've found that Film mode hold more detail in the highlights.

Shooting the same scene with the same exposure setting in Video and Film mode then applying the Rec.709 LUT in Resolve to the Film mode footage. The final image is very similar but there is more detail and dynamic range in the highlights.

Shoot ProRes/DnxHD in "Film" (log) mode (like log mode on most popular cinema cameras) for projects that may benefit from a bit more DR at the "expense" of some additional required work in post. BMCC log mode yields about a stop or so better DR than Rec.709. The BMCC's built-in LCD can be set to "Video" mode while recording "Film" mode to make shooting easier.

Shoot BMCC RAW CinemaDNG mode (which is always log) to capture the full DR & color range the camera is capable of recording. RAW is handled differently in post than is ProRes/DNxHD.

On a related note, there's information on how to use BMCC zebras when shooting ProRes in the following thread (read the whole thread):viewtopic.php?f=2&t=6722